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SAT Math skill page

SAT Quadratic Equations Practice

Handle SAT quadratic questions by recognizing roots, factors, parabolas, and the meaning of each solution.

Practice quadratic equations in DolphinPractice questions
14-20 min practice time3 questions on pageAdvanced Math
Practice time14-20 min
Question bank3 questions
Best forAdvanced Math

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
If x is positive and = 49, what is x?
  1. -7
  2. 0
  3. 7
  4. 49
Show answer and solution
Correct answerC. 7

Solution walkthrough

  1. The solutions to = 49 are x = 7 and x = -7.
  2. Since x is positive, x = 7.
Question 2 of 3Medium
If - 5x + 6 = 0, what is the sum of the two solutions?
  1. 2
  2. 3
  3. 5
  4. 6
Show answer and solution
Correct answerC. 5

Solution walkthrough

  1. Factor the equation as (x - 2)(x - 3) = 0, so the solutions are 2 and 3.
  2. Their sum is 5.
Question 3 of 3Hard
The height h, in feet, of a ball t seconds after launch is h = -16t^2 + 64t. After how many seconds does the ball return to the ground?
  1. 2
  2. 3
  3. 4
  4. 8
Show answer and solution
Correct answerC. 4

Solution walkthrough

  2. Factor to get -16t(t - 4) = 0, so t = 0 or t = 4.
  3. The return time after launch is 4 seconds.

Avoid these traps

Common mistakes on this skill

Forgetting the second solution

Quadratics can have two roots. Check whether the problem wants one root, both roots, or a contextual answer.

Dropping a negative sign

Factoring and expanding quadratics often hinge on signs. Test your factors by multiplying them back out.

Using a context-impossible root

In word problems, a negative time or length may be algebraically valid but not meaningful.

Study plan

How to practice this skill in Dolphin

  1. Memorize the factor patterns for simple trinomials.
  2. Practice setting each factor equal to zero after factoring.
  3. Connect roots to x-intercepts on a graph.
  4. For word problems, reject roots that do not make sense in context.
Practice quadratic equations in Dolphin

Related practice

Build the surrounding skills

SAT Linear Functions PracticeSAT Linear Equations PracticeSAT Geometry PracticeSAT Math skill hub

Skill cluster

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FAQ

Questions about SAT Quadratic Equations Practice

Do I need the quadratic formula for the SAT?

It can help, but many SAT quadratic questions are designed for factoring, graph interpretation, or simple structure recognition.

What is a root of a quadratic?

A root is an x-value that makes the quadratic equal zero. On a graph, roots are x-intercepts.

Why are quadratic word problems tricky?

They often produce more than one algebraic solution, and you have to decide which one fits the situation.